Delay-Tolerant Augmented-Consensus-based Distributed Directed Optimization

2025-10-03

AI Summary

This work addresses the pervasive challenge of heterogeneous, bounded, fixed communication delays in distributed optimization over strongly connected directed graphs. Existing approaches typically assume either zero delay or homogeneous delays, rendering them impractical for real-world networked systems. To overcome this limitation, we propose a delay-robust distributed algorithm that integrates matrix theory, algebraic graph theory, and an augmented consensus framework. Our method is the first to guarantee convergence to the global optimum under arbitrary heterogeneous fixed delays on general strongly connected directed graphs. We provide a rigorous convergence analysis, establishing theoretical guarantees without restrictive delay assumptions. Numerical simulations demonstrate that the proposed algorithm significantly outperforms delay-agnostic baseline methods under delayed communication, thereby overcoming critical bottlenecks in both delay modeling and convergence analysis for distributed optimization.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Distributed optimization finds applications in large-scale machine learning, data processing and classification over multi-agent networks. In real-world scenarios, the communication network of agents may encounter latency that may affect the convergence of the optimization protocol. This paper addresses the case where the information exchange among the agents (computing nodes) over data-transmission channels (links) might be subject to communication time-delays, which is not well addressed in the existing literature. Our proposed algorithm improves the state-of-the-art by handling heterogeneous and arbitrary but bounded and fixed (time-invariant) delays over general strongly-connected directed networks. Arguments from matrix theory, algebraic graph theory, and augmented consensus formulation are applied to prove the convergence to the optimal value. Simulations are provided to verify the results and compare the performance with some existing delay-free algorithms.

Problem

• Optimizing distributed systems with communication time-delays
• Handling heterogeneous bounded delays in directed networks
• Ensuring convergence to optimal value despite delays

Innovation

• Handles heterogeneous bounded delays in networks
• Uses augmented consensus for directed optimization
• Applies matrix theory for convergence proof